Does this seem like a meek, mild, moderate, gentle word to you? Results may vary. On the one hand it may meet you ever so gently like the Everly Brothers and their youthful but proper romantic laments, the sound of nice boys for whom things just don’t seem to work out but you know they’ll come even eventually and all will be loverly. But on the other hand it has that sound of peeve and evilly perhaps vermin and measly. That ee gives it the high wheedling /i/ sound, with a sense of diminution (and maybe even not merely that) and perhaps the buzz of an insect.
But that’s just how it seems to me. It’s not a word from my own dialect, so why should I expect to have a well developed taste for it? Just as you’re used to the foods and flavour profiles you grew up with, you’re used to the words and sounds you grew up with. I grew up eating cereal for breakfast, and a modest and unseemly morning repast might be corn flakes or oatmeal or – in my current years – a croissant. Those who grew up in Japan are more likely to have fish and other things that hardly seem fitting for breakfast to a whitebread Canadian. Even Anglophones from another place might expect different things. Bacon and eggs is almost extravagant to me, but those plus baked beans and fried tomato might go quite moderately, even modestly, in northern England, perhaps more so in earlier times.
And so too with words. I would not likely say or write “A’ wor goin’ up nice an’ meverly like,” let alone “Un aw thowt awd nare sin hur lookin more meeverly,” but those are two of the quotations for meeverly in the Oxford English Dictionary. It’s nearly universal that /i/ sounds smaller than /a/ or /ɛ/, and so either more endearing or more contemptible, when it comes down to matters of sound symbolism, but that doesn’t always play out equally everywhere, and not nearly all words are sound symbolic; there’s an immoderate amount of other influence. Words just don’t always mean what the naïve ear would expect them to mean, and what the naïve ear would expect them to mean varies from place to place.
So yes, this is a now-rare word, mainly from northern English dialects, meaning ‘moderately, mildly, gently, easily’. It’s not clear where it came from, but it’s much like meeterly, which in turn seems to be an altered form of meetly, which is an adverb from the adjective meet, which means ‘fitting, proper, suitable’, as in it is meet and right so to do (if that phrase sounds familiar you must be Anglican). It appears to have mutated immoderately from its origins. But it has risen to meet the need and feel of its time and place. Which may just not be here and now.
If you do wish to add this word to your usage, though, I hope you will use it meeverly.